Mallinckrodt Plc agreed to buy Questcor Pharmaceuticals Inc. for $5.6 billion to add specialty drugs in the latest industry deal that moves a U.S. company to Ireland for a lower tax rate.

Mallinckrodt, with its registered headquarters in Dublin and run from Hazelwood, Missouri, will pay cash and stock valued at $86.08 a share for Questcor, the companies said in a statement today. That’s 27 percent above the April 4 closing price for Anaheim, California-based Questcor.

The deal follows Mallinckrodt Chief Executive Officer Mark Trudeau’s strategy of investing money in the specialty pharmaceuticals business while reducing the company’s focus on medical imaging. In February Questcor’s shares plunged 23 percent over three days after a report questioned the quality of its autoimmune drug, H.P. Acthar Gel.

Questcor “was probably the most controversial name in the biopharma space,” said David Amsellem, an analyst with Piper Jaffray & Co. Yet Acthar still continues to sell well, he said in a telephone interview.

Generic and specialty drugmakers have been consolidating as companies including Mylan Inc. and Actavis Plc acquire assets, especially injectable specialty medications that are more difficult to manufacture and thus have fewer competitors.

Price Leverage

Mylan, for example, agreed last year to buy India’s Agila Specialties for $1.6 billion. The deals enable the companies to bring products to new markets and providers more leverage when negotiating prices with insurers and wholesalers.

Mallinckrodt in February agreed to buy Cadence Pharmaceuticals Inc. for $1.3 billion as part of its goal to be among the top 25 percent of specialty drug manufacturers.

“We are now well on our way to becoming a leader in the development and commercialization of specialty therapeutics around the world,” Trudeau said in today’s statement.

The tax rate on Questcor’s business will drop by about 10 percent, Mallinckrodt Chief Financial Officer Matthew Harbaugh said on a conference call today.

Questcor rose 20 percent to $80.94 at 10:15 a.m. New York time, while Mallinckrodt decreased 2.5 percent to $60.96. Questcor holders will receive $30 in cash and 0.897 of a Mallinckrodt share for each Questcor share they own.

The acquisition adds Questcor’s Acthar to Mallinckrodt’s range of branded and generic specialty medicines. Sales of the gel last year rose 50 percent to $761.3 million.

Increased Use

“Acthar has significantly durability in the marketplace, Trudeau said on the conference call. ‘‘We believe it will be very difficult for this product to be replicated in any way from a generic.’’

Mallinckrodt also makes the base ingredients in other medicines.

The deal is the latest example of a U.S. company moving offshore to take advantage of Ireland’s lower tax rate. Questcor, for example, paid a 35 percent tax rate in the last quarter of 2013, while Mallinckrodt paid 29 percent.